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Pathwise uniqueness for a class of SPDEs driven by cylindrical $\alpha$-stable processes

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arxiv 1703.00664 v1 pith:WBAEL67J submitted 2017-03-02 math.PR

Xiaobin Sun , Longjie Xie , Yingchao Xie This is my paper · ORCID
classification math.PR
keywords alphacylindricaldimensionaldrivenequationinfinitepathwisestable
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abstract

We show the pathwise uniqueness for stochastic partial differential equation driven by a cylindrical $\alpha$-stable process with H\"older continuous drift, thus obtaining an infinite dimensional generalization of the result of Priola [Osaka J. Math., 2012] in the case $H=\mathbb{R}^d$. The proof is based on an infinite dimensional Kolmogorov equation with non-local operator.

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